s
along the lines dividing the squares? The problem soon proved to be both
fascinating and bristling with difficulties. I present it in a
simplified form, taking a board of smaller dimensions.

[Illustration:

+---+---*---+---+ +---+---+---*---+ +---+---+---*---+
| | H | | | | | H | | | | H |
+---+---*---+---+ +---+---*===*---+ +---*===*---*---+
| | H | | | | H | | | H H H |
+---+---*---+---+ +---+---*---+---+ +---*---*---*---+
| | H | | | | H | | | H H H |
+---+---*---+---+ +---*===*---+---+ +---*---*===*---+
| | H | | | H | | | | H | | |
+---+---*---+---+ +---*---+---+---+ +---*---+---+---+

+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+

+---+---*---+---+ +---+---+---*---+ +---+---+---*---+
| | H | | | | | H | | | | H |
+---*===*---+---+ +---*===*===*---+ +---+---*===*---+
| H | | | | H | | | | | H | |
+---*===*===*---+ +---*===*===*---+ +---+---*---+---+
| | | H | | | | H | | | H | |
+---+---*===*---+ +---*===*===*---+ +---*===*---+---+
| | H | | | H | | | | H | | |
+---+---*---+---+ +---*---+---+---+ +---*---+---+---+

]

It is obvious that a board of four squares can only be so divided in one
way--by a straight cut down the centre--because we shall not count
reversals and reflections as different. In the case of a board of
sixteen squares--four by four--there are just six different ways. I have
given all these in the diagram, and the reader will not find any others.
Now, take the larger board of thirty-six squares, and try to discover in
how many ways it may be cut into two parts of the same size and shape.

289.--LIONS AND CROW